In a medium bowl, combine the matzo meal, oil, salt, pepper, and nigella seeds. Add 1 cup boiling water and mix well to incorporate. Add the egg, incorporating quickly to avoid partially cooking it. Using wet hands, form the dough into 12 equal-size disks and reserve.
In a medium bowl, combine the chicken, fennel, orgeat or almond extract, salt, and pepper. Using wet hands, form the mixture into 12 equal-size balls. Place a ball of filling on a matzo-meal disk and pinch and roll the edges together to form a ball. Repeat with remaining filling and matzo-meal disks.
Bring a large pot of salted water to a boil. Gently add the stuffed matzo balls, reduce heat, cover, and simmer until matzo balls are cooked through and float, 20 to 25 minutes.
Cook the Apples
In a medium saucepan over medium-high heat, heat the oil. Add the apples and sauté until slightly softened, about 5 minutes. Add the Calvados and stir, scraping up any bits on the bottom of the pan, until most of the Calvados has evaporated, about 2 minutes. Remove apples from pan and reserve.
Assemble the Soup
In a pot, heat the broth until just simmering. Divide the apples among four soup bowls, then ladle broth and matzo balls into each bowl. Garnish with nigella seeds before serving.
